Our aim is to continue and extend our theoretical, computational and experimental studies to assess how gene frequency data and quantitative measurements of traits associated with fitness can be used to make inferences on the forces acting on natural populations. The large and increasing body of data on genotypic frequencies in natural populations raises many important questions, in particular concerning the forces maintaining this variation and parameter values asssociated with these forces. In connection with these questions, we aim (1) to continue our consideration of tests of the theory that genetic variation at a given locus is "natural," (2) to assess the effects of linkage between loci, geographical patterns and historical factors on these tests, (3) to extend the range of current tests by finding asymptotic (i.e. large sample size) test procedures, (4) to extend work on the effects of selection in a random environment, (5) to continue the development of a certain model of the genome to re-evaluate the statistical analysis of classical experiments on the quantitative genetics of viability, (6) to extend the model to multiple loci, (7) to carry out experiments on ploidy levels and levels of inbreeding to examine predictions made by the model.